I would not use newspaper. Newspaper has a nasty odor to it and the ink will rub off on the inside of the cooler and anything else it touches. I think your t-shirts and blanket idea's the way to go.
Inside the humidors, if you don't have enough bubbly wrap, you can use inflated zipper bags. Just make sure it's tight enough so to prevent movement. If the humidors lock, lock them. If not, pack them tightly enough to where the lid won't be pushed open by the zippy bags.
The cooler idea for the dry house is a good one. It's virtually impossible to keep a wooden humidor from losing moisture in extremely dry climates. Of course, you can always increase the amount of media and service it more often, which is what I did. Eventually you'll probably end up in a wineador, which is what I did.